How do I add a bump map to a texture I made in blender?
CYCLES
In Node Editor Add two color textures (Image Texture nodes), set one as Color and the other as Non-Color Data. Connect the second one to the Height input of the Bump node (set the Strenght as you like). Plug it then to the Normal input of your Diffuse node.

BLENDER INTERNAL RENDER
Add two identical textures to separate texture slots. Call the second one BUMP. Under Influence uncheck Color checkbox. Check the Normal (set its value) and RGB to Intensity checkboxes.